The Church of St. Polyeuktos is easily overlooked, which is precisely what I did during my many earlier visits to the area. It lies in a park near a busy crossing, and pedestrians are invited to pass around it. Other traffic doe not even come close.
It was constructed in 524-527 by Anikia Juliana, the daughter of Aniklus Olybrius. Only the foundations have remained, they were revealed during excavations in 1964-1965, that became necessary after the construction of an underpass revealed them [The foundations were more impressive than what we see now as I saw on pictures of them, grass having overgrown much of them]. It exemplified the architecture of its era, and was built shortly before Emperor Justitian built the better-known Sergios Bakkhos and Hagias Sophia churches. It was a domed basilica, in a Greek Cross format, with the dome above the centre. Synthronon stairs were within the abcis.
During the excavations it became clear many of its parts were smuggled to the St. Marks church in Venice during the 13th century Crusade [such as column capitals and “dignities” (whatever the Turkish translator of the text on the information outside meant). It seems to have been in use until the 12th century, but was heavily damaged during the Latin invasion.

As for the latter statement, I tend to doubt if much extra harm was done, I found a text (see the care and maintenance part) "Princess Anicia Juliana commissioned Hagios Polyeuktos. She dedicated the church to Polyeuktos, a Roman soldier who lived in Melitene (modern Malatya) on the river Euphrates. He suffered martyrdom on 9 January 250. At an unknown point, his relics were transferred to Constantinople. A total of five churches are dedicated to him in the following cities: Melitene, Jerusalem, Ravenna, and two in Constantinople. Anicia Juliana chose to dedicate the church to Polyeuktos because the saint recalled her descent from Theodosius II, whose wife Eudocia had built the earlier church of Hagios Polyeuktos in Constantinople.

The church originally stood on the Mese, the main street in Late Antique Constantinople. Only decorative fragments and the substructures of the church remain. Included among these decorative fragments is an inscription which encircled the naos of the church and the narthex. The Greek Anthology 1.10 records the 76 line epigram found in the church of the martyr Polyeuktos, although not in the order in which it was situated in the church. Most of our knowledge concerning the architectural form of the church is derived from the epigram. The church was a basilica and had a gallery. The columns supported a gilded roof. The church included arched recesses and may have included a transept terminating in the semicircular apse. The walls were decorated with colored marble, and a representation of Constantine’s baptism was found in the narthex or courtyard. The excavations uncovered the foundations of the apse, nave, aisles, narthex, atrium, and other substructures of the church, as well as a crypt and burials.

References are made about the church in the tenth and eleventh centuries, but there is no information regarding its upkeep, administration, and status. Since the excavations uncovered no major modifications or additions to its fabric or decoration but did uncover deposits of dumped material from the seventh to the tenth centuries, this suggests that the church was kept on a “care and maintenance” basis only.

Until the completion of Justinian’s Hagia Sophia, the basilica eclipsed all other churches in size and splendor. Both the poem and the church make an explicit political statement about the noble lineage of Anicia Juliana."

At least one part is now in the Arch. Museum.